{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "using Polynomials, PyPlot, QuadGK, LinearAlgebra"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "# Dot products of functions\n",
    "\n",
    "We can apply the Gram–Schmidt process to *any* vector space as long as we **define a dot product** (also called an **inner product**).   (Technically, a continuous (\"complete\") vector space equipped with an inner product is called a **Hilbert space**.)\n",
    "\n",
    "For column vectors, the usual dot product is to multiply the components and add them up.\n",
    "\n",
    "But (real-valued) *functions* $f(x)$ also define a vector space (you can add, subtract, and multiply by constants).  In particular, consider functions defined on the interval $x \\in [-1,1]$.   The \"components\" of $f$ can be viewed as its *values* $f(x)$ at each point in the domain, and the obvious analogue of \"summing the components\" is the **integral**.   Hence, the most obvious \"dot product\" of two functions in this space is:\n",
    "\n",
    "$$\n",
    "f \\cdot g = \\int_{-1}^1 f(x) g(x) \\, dx\n",
    "$$\n",
    "\n",
    "Such a generalized inner product is commonly denoted $\\langle f, g \\rangle$ (or $\\langle f | g \\rangle$ in physics).\n",
    "\n",
    "This satisfies the [key properties](https://en.wikipedia.org/wiki/Inner_product_space#Elementary_properties) of dot products that make linear algebra \"work\":\n",
    "\n",
    "* **symmetry**: $f \\cdot g = g \\cdot f$\n",
    "* **linearity**: $f \\cdot (\\alpha g + \\beta h) = \\alpha (f\\cdot g) + \\beta (f \\cdot h)$\n",
    "* **positivity**: $f \\cdot f = \\Vert f \\Vert^2 \\ge 0$, and $=0$ only if $f = 0$ ([almost everywhere](https://en.wikipedia.org/wiki/Almost_everywhere)).\n",
    "\n",
    "As long as the dot product has these properties, much of what we do in 18.06 will \"just work\" for functions too.  **Gram–Schmidt will just work**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Orthogonal polynomials\n",
    "\n",
    "In particular, let us consider a subspace of functions defined on $[-1,1]$: **polynomials** $p(x)$ (of any degree).\n",
    "\n",
    "One possible basis of polynomials is simply:\n",
    "\n",
    "$$\n",
    "{1, x, x^2, x^3, \\ldots}\n",
    "$$\n",
    "\n",
    "(There are infinitely many polynomials in this basis because this vector space is **infinite-dimensional**.)\n",
    "\n",
    "Instead, let us apply Gram–Schmidt to this basis in order to get an **orthogonal basis of polynomials** known as the [Legendre polynomials](https://en.wikipedia.org/wiki/Legendre_polynomials)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Julia code\n",
    "\n",
    "I'll use the [Polynomials package](https://github.com/Keno/Polynomials.jl) to do polynomial arithmetic for me.\n",
    "\n",
    "However, I'll need to define a few extra methods to perform my dot products from above, and I also want to display (\"pretty print\") the polynomials a bit more nicely than the default."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "polydot (generic function with 1 method)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# compute the dot product ⟨p,q⟩ = ∫p(x)q(x) on [-1,1]\n",
    "polydot(p::Polynomial, q::Polynomial) = integrate(p*q, -1,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# force IJulia to display as LaTeX rather than HTML\n",
    "Base.showable(::MIME\"text/html\", ::Polynomial) = false"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$3 + 4\\cdot x + 5\\cdot x^{2} + 6\\cdot x^{3}$"
      ],
      "text/plain": [
       "Polynomial(3 + 4*x + 5*x^2 + 6*x^3)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Polynomial([3,4,5,6])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$9 + 24\\cdot x + 46\\cdot x^{2} + 76\\cdot x^{3} + 73\\cdot x^{4} + 60\\cdot x^{5} + 36\\cdot x^{6}$"
      ],
      "text/plain": [
       "Polynomial(9 + 24*x + 46*x^2 + 76*x^3 + 73*x^4 + 60*x^5 + 36*x^6)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Polynomial([3,4,5,6])^2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Gram–Schmidt on polynomials\n",
    "\n",
    "Now, let's apply Gram–Schmidt on the polynomials $a_i = x^i$ for $i = 0, 1, \\ldots$.\n",
    "\n",
    "Ordinarily, in Gram–Schmidt, I would normalize each result $p(x)$ by dividing by $\\Vert p \\Vert = \\sqrt{p \\cdot p}$, but that will result in a lot of annoying square roots.  Instead, I will divide by $p(1)$ to result in the more conventional Legendre polynomials.  **This is not an \"orthonormal\" basis because we have chosen a different normalization, but it is still an *orthogonal* basis.**\n",
    "\n",
    "That means that to get $p_i(x)$, I will do:\n",
    "\n",
    "$$\n",
    "v_i(x) = a_i(x) - \\sum_{j=0}^{i-1} p_j(x) \\frac{p_j \\cdot a_i}{p_j \\cdot p_j}\n",
    "$$\n",
    "\n",
    "We would get an ordinary orthnormal basis of polynomials with\n",
    "\n",
    "$$\n",
    "q_i(x) = v_i(x) / \\Vert v_i \\Vert\n",
    "$$\n",
    "\n",
    "but instead we will use the Legendre normalization\n",
    "\n",
    "$$\n",
    "p_i(x) = v_i(x) / v_i(1)\n",
    "$$\n",
    "\n",
    "\n",
    "where I explicitly divide by $p_i \\cdot p_i$ in the projections to compensate for the lack of normalization.\n",
    "\n",
    "In Julia, I will use the special syntax `2 // 3` to construct the exact rational $\\frac{2}{3}$, etc.  This will allow me to see the exact Legendre polynomials without any roundoff errors or annoying decimals."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$1$"
      ],
      "text/plain": [
       "Polynomial(1//1)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p0 = a0 = Polynomial([1//1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$x$"
      ],
      "text/plain": [
       "Polynomial(x)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a1 = Polynomial([0, 1//1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$x$"
      ],
      "text/plain": [
       "Polynomial(x)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p1 = a1 - p0 * polydot(p0, a1) // polydot(p0, p0)\n",
    "p1 = p1 / p1(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0//1"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "polydot(p0, a1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Orthogonalization didn't change $x$, because $x$ and $1$ are already orthogonal under this dot product.  In fact, any even power of $x$ is orthogonal to any odd power (because the dot product is the integral of an even function times an odd function).\n",
    "\n",
    "On the other hand, $x^2$ and $1$ are *not* orthogonal, so orthogonalizing them leads to a *different* polynomial of degree 2:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$x^{2}$"
      ],
      "text/plain": [
       "Polynomial(x^2)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a2 = Polynomial([0, 0, 1//1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$-\\frac{1}{2} + \\frac{3}{2}\\cdot x^{2}$"
      ],
      "text/plain": [
       "Polynomial(-1//2 + 3//2*x^2)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p2 = a2 - p0 * polydot(p0, a2) // polydot(p0, p0) -\n",
    "          p1 * polydot(p1, a2) // polydot(p1, p1)\n",
    "p2 = p2 / p2(1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It quickly gets tiresome to type in these expressions one by one, so let's just write a function to compute the Legendre polynomials $p_0, \\ldots, p_n$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "legendre_gramschmidt (generic function with 1 method)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function legendre_gramschmidt(n)\n",
    "    legendre = [Polynomial([1//1])]\n",
    "    for i = 1:n\n",
    "        p = Polynomial([k == i ? 1//1 : 0//1 for k=0:i])\n",
    "        for q in legendre\n",
    "            p = p - q * (polydot(q, p) // polydot(q,q))\n",
    "        end\n",
    "        push!(legendre, p / p(1))\n",
    "    end\n",
    "    return legendre\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6-element Vector{Polynomial{Rational{Int64}, :x}}:\n",
       " Polynomial(1//1)\n",
       " Polynomial(x)\n",
       " Polynomial(-1//2 + 3//2*x^2)\n",
       " Polynomial(-3//2*x + 5//2*x^3)\n",
       " Polynomial(3//8 - 15//4*x^2 + 35//8*x^4)\n",
       " Polynomial(15//8*x - 35//4*x^3 + 63//8*x^5)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "L = legendre_gramschmidt(5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's display them more nicely with LaTeX:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$1$"
      ],
      "text/plain": [
       "Polynomial(1//1)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$x$"
      ],
      "text/plain": [
       "Polynomial(x)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$-\\frac{1}{2} + \\frac{3}{2}\\cdot x^{2}$"
      ],
      "text/plain": [
       "Polynomial(-1//2 + 3//2*x^2)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$-\\frac{3}{2}\\cdot x + \\frac{5}{2}\\cdot x^{3}$"
      ],
      "text/plain": [
       "Polynomial(-3//2*x + 5//2*x^3)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\frac{3}{8} - \\frac{15}{4}\\cdot x^{2} + \\frac{35}{8}\\cdot x^{4}$"
      ],
      "text/plain": [
       "Polynomial(3//8 - 15//4*x^2 + 35//8*x^4)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\frac{15}{8}\\cdot x - \\frac{35}{4}\\cdot x^{3} + \\frac{63}{8}\\cdot x^{5}$"
      ],
      "text/plain": [
       "Polynomial(15//8*x - 35//4*x^3 + 63//8*x^5)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display.(L);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Key things to notice:\n",
    "\n",
    "* The polynomials contain *only even* or *only odd* powers of $x$, but not both.  The reason is that the even and odd powers of $x$ are *already* orthogonal under this dot product, as noted above.\n",
    "\n",
    "* A key property of Gram–Schmidt is that the **first k vectors span the same space** as the **original first k vectors**, for any k.   In this case, it means that $p_0, \\ldots, p_k$ span the same space as $1, x, \\ldots, x^k$.  That is, the $p_0, \\ldots, p_k$ polynomials are an **orthogonal basis for all polynomials of degree k or less**.\n",
    "\n",
    "These polynomials are **very special** in many ways.  To get a hint of that, let's plot them:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "┌ Warning: `vendor()` is deprecated, use `BLAS.get_config()` and inspect the output instead\n",
      "│   caller = npyinitialize() at numpy.jl:67\n",
      "└ @ PyCall /Users/stevenj/.julia/packages/PyCall/L0fLP/src/numpy.jl:67\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "PyObject Text(0.5, 1.0, 'Legendre polynomials')"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "leg = []\n",
    "x = range(-1, 1, length=300)\n",
    "for i in eachindex(L)\n",
    "    plot(x, L[i].(x), \"-\")\n",
    "    push!(leg, L\"P_{%$(i-1)}(x)\")\n",
    "end\n",
    "plot(x, x * 0, \"k--\")\n",
    "legend(leg)\n",
    "xlabel(L\"x\")\n",
    "title(\"Legendre polynomials\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that $p_n(x)$ has exactly $n$ roots in the interval $[-1,1]$!\n",
    "\n",
    "This is essentially required by the fact that they are orthogonal: $p_n$ has to oscillate in sign faster and faster in $[-1,1]$ as $n$ increases in order to integrate to zero against the previous polynomials."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Expanding a polynomial in the Legendre basis.\n",
    "\n",
    "Now that we have an orthogonal (but not orthonormal) basis, it is easy to take an arbitrary polynomial $p(x)$ and write it in this basis:\n",
    "\n",
    "$$\n",
    "    p(x) = \\alpha_0 p_0(x) + \\alpha_1 p_1(x) + \\cdots = \\sum_{i=0}^\\infty \\alpha_i p_i(x)\n",
    "$$\n",
    "\n",
    "because we can get the coefficients $\\alpha_i$ merely by projecting:\n",
    "\n",
    "$$\n",
    "\\alpha_i = \\frac{p_i \\cdot p}{p_i \\cdot p_i}\n",
    "$$\n",
    "\n",
    "Note, however, that this isn't actually an infinite series: if the polynomial $p(x)$ has degree $d$, then $\\alpha_i = 0$ for $i > d$.  The polynomials $p_0, \\ldots, p_d$ are a basis for the subspace of polynomials of degree $d$ (= span of $1, x, \\ldots, x^d$)!\n",
    "\n",
    "Let's see how this works for a \"randomly\" chosen $p(x)$ of degree 5:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$1 + 3\\cdot x + 4\\cdot x^{2} + 7\\cdot x^{3} + 2\\cdot x^{4} + 5\\cdot x^{5}$"
      ],
      "text/plain": [
       "Polynomial(1 + 3*x + 4*x^2 + 7*x^3 + 2*x^4 + 5*x^5)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p = Polynomial([1,3,4,7,2,5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here are the coefficients α:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6-element Vector{Rational{Int64}}:\n",
       "  41//15\n",
       " 327//35\n",
       "  80//21\n",
       " 226//45\n",
       "  16//35\n",
       "  40//63"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "α = [polydot(q,p)/polydot(q,q) for q in L]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's check that the sum of $\\alpha_i p_i(x)$ gives $p(x)$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$1 + 3\\cdot x + 4\\cdot x^{2} + 7\\cdot x^{3} + 2\\cdot x^{4} + 5\\cdot x^{5}$"
      ],
      "text/plain": [
       "Polynomial(1//1 + 3//1*x + 4//1*x^2 + 7//1*x^3 + 2//1*x^4 + 5//1*x^5)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum(α .* L) # α[1]*L[1] + α[2]*L[2] + ... + α[6]*L[6]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$0//1$"
      ],
      "text/plain": [
       "Polynomial(0//1)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum(α .* L) - p"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Polynomial fits\n",
    "\n",
    "### Review: Projections and Least-Square\n",
    "\n",
    "Given a matrix $Q$ with $n$ orthonormal columns $q_i$, we know that the **orthogonal projection** \n",
    "\n",
    "$$\n",
    "p = QQ^T b = \\sum_{i=1}^n q_i q_i^T b\n",
    "$$\n",
    "\n",
    "is the **closest vector** in $C(Q)$ to $b$.  That is, it **minimizes** the distance:\n",
    "\n",
    "$$\n",
    "\\min_{p \\in C(Q)} \\Vert p - b \\Vert \\; .\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Closest polynomials\n",
    "\n",
    "Now, suppose that we have some function $f(x)$ on $x\\in[-1,1]$ that is *not* a polynomial, and we want to find the **closest polynomial** of degree $n$ to $f(x)$ in the least-square sense.  That is, we want to find the polynomials $p(x)$ of degree $n$ that **minimizes**\n",
    "\n",
    "$$\n",
    "\\min_{p\\in \\mathcal{P}_n} \\int_{-1}^1 |f(x)-p(x)|^2 dx = \n",
    "\\min_{p\\in \\mathcal{P}_n} \\Vert f(x) - p(x) \\Vert^2\n",
    "$$\n",
    "\n",
    "where\n",
    "\n",
    "$$\n",
    "\\mathcal{P}_n = \\operatorname{span} \\{ 1, x, x^2, \\ldots, x^n \\}\n",
    "= \\operatorname{span} \\{ p_0(x), p_1(x), \\ldots, p_n(x) \\}\n",
    "$$\n",
    "\n",
    "is the space of polynomials of degree $\\le n$, spanned by our Legendre polynomials up to degree $n$.\n",
    "\n",
    "Presented in this context, we can see that this is *the same problem*  as our least-square problem above, and the solution should be the same: $p(x)$ is the **orthogonal projection** of $f(x)$ onto $\\mathcal{P}_n$, given by:\n",
    "\n",
    "$$\n",
    "p(x) = p_0(x) \\frac{p_0 \\cdot f}{p_0 \\cdot p_0} + \\cdots \n",
    "       p_n(x) \\frac{p_n \\cdot f}{p_n \\cdot p_n} \\; .\n",
    "$$\n",
    "\n",
    "Let's try this out for $f(x) = e^x$.  Because we're lazy, we'll have Julia compute the integrals numerically using its `quadgk` function, and fit it to polynomials of degree 5 using our Legendre polynomials from above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "polydot (generic function with 2 methods)"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "polydot(p::Polynomial, f::Function) = quadgk(x -> p(x)*f(x), -1,1, atol=1e-13, rtol=1e-11)[1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, let's use dot products to compute the coefficients in the $p_i(x)$ expansion above for $f(x) = e^x$ (the `exp` function in Julia):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6-element Vector{Float64}:\n",
       " 1.1752011936438014\n",
       " 1.1036383235143268\n",
       " 0.35781435064737244\n",
       " 0.07045563366848885\n",
       " 0.00996512814886882\n",
       " 0.0010995861272082227"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "coeffs = [polydot(p,exp)/polydot(p,p) for p in L]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One thing to notice is an important fact: expanding functions, especially [smooth functions](https://en.wikipedia.org/wiki/Smoothness), in orthogonal bases like Legendre polynomials or Fourier series tends to converge very rapidly.\n",
    "\n",
    "Let's write out the resulting polynomial $p(x)$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$1.000030941375941 + 1.000016597000109\\cdot x + 0.49935229541280063\\cdot x^{2} + 0.16651770555815018\\cdot x^{3} + 0.043597435651301086\\cdot x^{4} + 0.008659240751764753\\cdot x^{5}$"
      ],
      "text/plain": [
       "Polynomial(1.000030941375941 + 1.000016597000109*x + 0.49935229541280063*x^2 + 0.16651770555815018*x^3 + 0.043597435651301086*x^4 + 0.008659240751764753*x^5)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p = sum(coeffs .* L)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's plot it:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "PyObject Text(0.5, 1.0, 'fitting $e^x$ to a degree-5 polynomial')"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(x, exp.(x), \"r-\")\n",
    "plot(x, p.(x), \"b--\")\n",
    "legend([L\"e^x\", L\"fit $p(x)$\"])\n",
    "xlabel(L\"x\")\n",
    "title(L\"fitting $e^x$ to a degree-5 polynomial\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "They are so close that you can hardly tell the difference!\n",
    "\n",
    "Let's plot the fits for degree 0, 1, …, 3 so that we can watch it converge:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "PyObject Text(0.5, 1.0, 'fitting $e^x$ to polynomials')"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(x, exp.(x), \"k--\")\n",
    "for n = 1:4\n",
    "    plot(x, sum([polydot(p,exp)/polydot(p,p) for p in L[1:n]] .* L[1:n]).(x), \"-\")\n",
    "end\n",
    "legend([L\"e^x\", [\"degree $i\" for i=0:3]...])\n",
    "xlabel(L\"x\")\n",
    "title(L\"fitting $e^x$ to polynomials\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By degree 3, it is hard to tell the difference from $e^x$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fitting a non-smooth function\n",
    "\n",
    "It may not be so surprising that we can fit $e^x$ to polynomials; after all, $e^x$ has a convergent Taylor series, which is also a polynomial. But what we try to fit a *non-smooth* function, such as a **triangle-shape function** $t(x)$?  That is,\n",
    "\n",
    "\n",
    "$$\n",
    "t(x) = 1 - |x|\n",
    "$$\n",
    "\n",
    "(a triangle peaked at $x=0$ and zero at $x=\\pm 1$).  Let's see:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "PyObject Text(0.5, 1.0, 'fitting a triangle-shape function to polynomials')"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t(x) = 1 - abs(x)\n",
    "\n",
    "L16 = legendre_gramschmidt(16) # compute a few more terms\n",
    "\n",
    "plot(x, t.(x), \"k--\")\n",
    "N = [1:2:16;]\n",
    "for n in N\n",
    "    plot(x, sum([polydot(p,t)/polydot(p,p) for p in L16[1:n]] .* L16[1:n]).(x), \"-\")\n",
    "end\n",
    "legend([L\"t(x)\", [\"degree $i\" for i in N .- 1]...])\n",
    "xlabel(L\"x\")\n",
    "title(\"fitting a triangle-shape function to polynomials\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is still converging, just much more slowly!"
   ]
  }
 ],
 "metadata": {
  "@webio": {
   "lastCommId": null,
   "lastKernelId": null
  },
  "kernelspec": {
   "display_name": "Julia 1.7.1",
   "language": "julia",
   "name": "julia-1.7"
  },
  "language_info": {
   "file_extension": ".jl",
   "mimetype": "application/julia",
   "name": "julia",
   "version": "1.7.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
